We watched this 2016 movie on HBO Max last night. It’s a story of a young woman struggling with Alcohol Use Disorder (AUD) that leads to her loss of her relationship with her significant other and a return to her now shuttered childhood home. The story has what might be considered magical symbolism – she has a connection to a reptilian Kaiju that attacks Soeul Korea. Her childhood frenemy has a similar AlterEgo that manifests as a towering, Yeager-like robot.
What our protagonist experiences as her banal life is manifest in Soeul as mayhem inflicted by the Kaiju – with the attendant loss of hundreds of lives as her Kaiju attacks the city. At this point in the movie, I was thinking sympathetic magic – like sticking pins into a Voodoo doll and expecting the person of whom the doll is an effigy to experience wounds and pain. Then it occurred to me that this was a movie about Math!
Math, you say? Yep, Math. I remembered my senior high school class in Elementary Analysis. There are mathematical transformations that we can perform on graphs or sets of points that can map a set from one space to another. The simplest transformations are translation and rotation. Take a circle drawn on a grid and move it up or down or left or right; that’s translation. It still looks like a circle. Take a triangle on a similar grid and spin it clockwise or counterclockwise. It still looks like a triangle. The lengths of its three sides and its angles are perfectly preserved; that’s rotation. These are special Affine Transformations, manipulations of a set of points that preserve the distance between points as well as the angles of lines in the figure. In other words, these particular transformations affect the orientation but not the shape of the figure.
But there are other affine transformations that do not preserve these things. Take scaling for instance – magnifying or reducing the size of a thing so that its shape is preserved but not its size – a model train is the perfect example. It may look identical to the life-sized train, but don’t expect it to carry the same load. Another affine transformation is reflection – producing a mirror image of a thing. Both scaling and reflection transforms yield a figure that is similar to the original, but it is not the same. The transformed figure has affinity for its original (from whence the Latin name affine).
My favorite examples of affine transforms are Salvador Dali’s melting clocks in The Persistence of Memory. The clock images have an affinity for actual clocks, but they are something else. Similarly, the relationship of the alcohol-impaired protagonist in Colossal to her Kaiju self is an affine transform.
The plot resolves when our protagonist flies to Soeul to protect the people from her antagonist’s robot monster. As she appears in Soeul, her Kaiju self appears in her hometown in what may be thought of as a reflection type affine transformation. Her Kaiju confronts her childhood frenemy, now a full-fledged nemesis, and she brings the conflict to an end.
You may be thinking something along the lines of, “What a total nerd. He can’t even watch a movie without doing a mathematical analysis.” If so, you are right.